Question

(a) name the vertex of ∠pmn. (b) write two other names for ∠qmp. (c) name the sides of ∠1.

Explanation:

Step1: Recall vertex definition

The vertex of an angle is the common endpoint of the rays that form the angle. For ∠PMN, the common endpoint of rays MP and MN is M.

Step2: Find other angle - naming conventions

An angle can be named by the vertex alone (if there is no ambiguity) or by three points with the vertex in the middle. For ∠QMP, two other names are ∠PMQ and ∠M (since there is no other angle at vertex M that would cause confusion in this context).

Step3: Identify angle - side rays

The sides of an angle are the two rays that form the angle. For ∠1 which is ∠NMQ, the sides are ray MN and ray MQ.

Answer:

(a) M
(b) ∠PMQ, ∠M
(c) Ray MN, Ray MQ